This depends on a number of factors, such as the degree of control the principal has over the agent, the degree to which the agent is integrated into the principal’s business and whether the agent deals with the principal’s customers in his own name.
Very broadly, if you appoint an individual as agent, he or she works only for you, you have the required permission from the FCA for the agent's activities, the contract sets out effective measures for you to control the agent, you accept full responsibility for the conduct of the agent and the agent makes clear to customers that it is representing you.